DISTRIBUTED SYSTEMS Principles and Paradigms Second Edition ANDREW S DISTRIBUTED SYSTEMS Principles and Paradigms Second Edition ANDREW S. TANENBAUM MAARTEN VAN STEEN Chapter 6 Synchronization (skip 6.4) Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

6.1 Clock Synchronization Physical Clock Logical Clock Vector Clock Figure 6-1. When each machine has its own clock, an event that occurred after another event may nevertheless be assigned an earlier time. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Figure 6-2. Computation of the mean solar day. Physical Clocks (1) Figure 6-2. Computation of the mean solar day. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Physical Clocks (2) Based on transitions of the Cesium 133 atom Universal Coordinated Time Figure 6-3. TAI (international Atomic Time) seconds are of constant length, unlike solar seconds. Leap seconds are introduced when necessary to keep in phase with the sun. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Global Positioning System (1) Real world facts that complicate GPS It takes a while before data on a satellite’s position reaches the receiver. The receiver’s clock is generally not in synch with that of a satellite. Figure 6-4. Computing a position in a two-dimensional space. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Global Positioning System (2) • ∆r is unknown deviation of the receiver’s clock • xr, yr, zr are unknown coordinates of the receiver • Ti is timestamp on a message from satellite i • ∆i = (Tnow − Ti) + ∆r is measured delay of the message sent by satellite i • Measured distance to satellite i: c × ∆i (c is speed of light) • Real distance is di =SQRT( (xi − xr)2 + (yi − yr)2 + (zi − zr)2 ) 4 satellites ⇒ 4 equations in 4 unknowns (with ∆r as one of them): di + c ∆r = c ∆i Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Clock Synchronization Algorithms Suppose there is a clock in machine p that ticks on each timer interrupt. Denote the value of that clock by Cp(t), where t is UTC time. • Ideally, we have that for each machine p, Cp(t) = t, or, in other words, dC/dt = 1. In practice: 1−ρ ≤ dC/dt ≤ 1+ ρ Goal: Never let two clocks in any system differ by more than δ time units ⇒ synchronize at least every δ/(2ρ) seconds. Figure 6-5. The relation between clock time and UTC when clocks tick at different rates. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Figure 6-6. Getting the current time from a time server at least once Network Time Protocol Figure 6-6. Getting the current time from a time server at least once every δ/(2ρ) seconds. Alternative: Let the time server (hierarchical stratum reference clock) scan all machines periodically, calculate an average, and inform each machine how it should adjust its time relative to its present time. Note: setting the time back is never allowed. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

The Berkeley Algorithm (1) Figure 6-7. (a) The time daemon asks all the other machines for their clock values. Figure 6-7. (c) The time daemon tells everyone how to adjust their clock. Figure 6-7. (b) The machines answer. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Clock Synchronization in Wireless Networks Figure 6-8. (a) The usual critical path in determining network delays. Figure 6-8. (b) The critical path in the case of RBS (Reference Broadcast Synchronization). P.243 Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

6.2.1 Lamport’s Logical Clocks (1) The "happens-before" relation → can be observed directly in two situations: If a and b are events in the same process, and a occurs before b, then a → b is true. If a is the event of a message being sent by one process, and b is the event of the message being received by another process, then a → b If a→b and b→c, then a→c → is a partial ordering of events Lamport’s Logical Clock attaches a timestamp C(e) to each event e such that if a→b then C(a) < C(b) Each message carries the sending time according to the sender’s clock Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Lamport’s Logical Clocks (2) Updating counter Ci for process Pi Before executing an event Pi executes Ci ← Ci + 1. When process Pi sends a message m to Pj, it sets m’s timestamp ts(m) equal to Ci after having executed the previous step. Upon the receipt of a message m, process Pj adjusts its own local counter as Cj ← max{Cj , ts(m)}, after which it then executes the first step and delivers the message to the application. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Lamport’s Logical Clocks (3) Figure 6-9. (a) Three processes, each with its own clock. The clocks run at different rates. Figure 6-9. (b) Lamport’s algorithm corrects the clocks. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Lamport’s Logical Clocks (4) Figure 6-10. The positioning of Lamport’s logical clocks in distributed systems. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Example: Totally Ordered Multicasting Figure 6-11. Updating a replicated database and leaving it in an inconsistent state. This case requires a totally-ordered multicast, which could be implemented by Lamport’s logical clock and an acknowledged message queue. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

6.2.2 Vector Clocks (1) Lamport’s clocks do not guarantee that if C(a) < C(b) that a causally preceded b Figure 6-12. Concurrent message transmission using logical clocks. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Vector Clocks (2) Vector clocks are constructed by letting each process Pi maintain a vector VCi with the following two properties: VCi [ i ] is the number of events that have occurred so far at Pi. In other words, VCi [ i ] is the local logical clock at process Pi . If VCi [ j ] = k then Pi knows that k events have occurred at Pj. It is thus Pi’s knowledge of the local time at Pj . Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Vector Clocks (3) Steps carried out to accomplish property 2 of previous slide: Before executing an event Pi executes VCi [ i ] ← VCi [i ] + 1. When process Pi sends a message m to Pj, it sets m’s (vector) timestamp ts(m) equal to VCi after having executed the previous step. Upon the receipt of a message m, process Pj adjusts its own vector by setting VCj [k ] ← max{VCj [k ], ts(m)[k ]} for each k, after which it executes the first step and delivers the message to the application. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Causally Ordered Multicasting Observation: We can now ensure that a message is delivered only if all causally preceding messages have already been delivered. Adjustment: Pi increments VCi[i] only when sending a message, and Pj “adjusts” VCj when receiving a message (i.e., effectively does not change VCj[j]). Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Enforcing Causal Communication Figure 6-13. Enforcing causal communication. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

6.3 Mutual Exclusion A Centralized Algorithm Figure 6-14. (c) When process 1 releases the resource, it tells the coordinator, which then replies to 2. Figure 6-14. (b) Process 2 then asks permission to access the same resource. The coordinator does not reply. Figure 6-14. (a) Process 1 asks the coordinator for permission to access a hared resource. Permission is granted. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

A Distributed Algorithm (1) Three different cases: If the receiver is not accessing the resource and does not want to access it, it sends back an OK message to the sender. If the receiver already has access to the resource, it simply does not reply. Instead, it queues the request. If the receiver wants to access the resource as well but has not yet done so, it compares the timestamp of the incoming message with the one contained in the message that it has sent everyone. The lowest one wins. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

A Distributed Algorithm (2) Figure 6-15. (c) When process 0 is done, it sends an OK also, so 2 can now go ahead. Figure 6-15. (a) Two processes want to access a shared resource at the same moment. Figure 6-15. (b) Process 0 has the lowest timestamp, so it wins. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

A Token Ring Algorithm Figure 6-16. (a) An unordered group of processes on a network. (b) A logical ring constructed in software. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

A Comparison of the Four Algorithms Figure 6-17. A comparison of three mutual exclusion algorithms. Skip 6.4 Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

6.5 Election Algorithms The Bully Algorithm P sends an ELECTION message to all processes with higher numbers. If no one responds, P wins the election and becomes coordinator. If one of the higher-ups answers, it takes over. P’s job is done. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

The Bully Algorithm (1) Figure 6-20. The bully election algorithm. (a) Process 4 holds an election. (b) Processes 5 and 6 respond, telling 4 to stop. (c) Now 5 and 6 each hold an election. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

The Bully Algorithm (2) Figure 6-20. The bully election algorithm. (d) Process 6 tells 5 to stop. (e) Process 6 wins and tells everyone. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Figure 6-21. Election algorithm using a ring. A Ring Algorithm Figure 6-21. Election algorithm using a ring. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Elections in Wireless Environments Figure 6-22. Election algorithm in a wireless network, with node a as the source. (a) Initial network. (b)–(e) The build-tree phase. (f) Reporting of best node to source. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Elections in Large-Scale Systems (1) Requirements for superpeer selection: Normal nodes should have low-latency access to superpeers. Superpeers should be evenly distributed across the overlay network. There should be a predefined portion of superpeers relative to the total number of nodes in the overlay network. Each superpeer should not need to serve more than a fixed number of normal nodes. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5

Elections in Large-Scale Systems (2) DHT: Reserve a fixed part of the ID space for superpeers. Example: if S superpeers are needed for a system that uses m-bit identifiers, simply reserve the k = ⌈log2 S⌉ leftmost bits for superpeers. Routing to superpeer: Send message for key p to node responsible for p AND 11· · ·1100· · ·00 Figure 6-23. Moving tokens in a two-dimensional space using repulsion forces. Tanenbaum & Van Steen, Distributed Systems: Principles and Paradigms, 2e, (c) 2007 Prentice-Hall, Inc. All rights reserved. 0-13-239227-5